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Edge Maximal Graphs of Branchwidth k: The k-Branches

Christophe Paul 1 Jan Arne Telle 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Treewidth and branchwidth are two closely related connectivity parameters of graphs. Graphs of treewidth at most k have well-known alternative characterizations as subgraphs of chordal graphs and as partial k-trees. In this paper we give analogous alternative characterizations for graphs of branchwidth at most k. We first show that they are the subgraphs of chordal graphs where every maximal clique X has three subsets of size at most k each such that any two subsets have union X, with the property that every minimal separator contained in X is contained in one of the three subsets. Secondly, we give a characterization of the edge-maximal graphs of branchwidth k, that we call k-branches.
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Submitted on : Thursday, March 26, 2009 - 9:53:30 PM
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Christophe Paul, Jan Arne Telle. Edge Maximal Graphs of Branchwidth k: The k-Branches. Discrete Mathematics, Elsevier, 2009, 309 (6), pp.1467-1475. ⟨10.1016/j.disc.2008.02.030⟩. ⟨lirmm-00371208⟩



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